Islamic State on Tuesday evening claimed responsibility for an attack on a Christmas market that killed 12 people in Berlin on Monday, as police warned that the attacker could still be armed and at large.

The IS group released a statement through its propaganda arm, the Amaq agency, in which it claimed responsibility for the attack.

The claim came after German police on Tuesday released a man who was arrested following Monday's attack on a Christmas market in Berlin, saying they had insufficient evidence to continue holding him - nobody else is currently in custody over the attack.

The man, a Pakistani national, entered Germany last year as an asylum seeker - he was arrested two kilometres from the market in Breitscheidplatz after a haulage truck ploughed through crowds of Christmas shoppers, leaving 12 people dead and 48 wounded.

Friends of the man, named as Naved B, said no ammunition was found when police searched his residence.

He is reportedly from the Baloch minority in Pakistan - there were delays in interrogating him as he only speaks the Baloch language and there were no translators available.

"The investigation up to now did not yield any urgent suspicion against the accused," the prosecutor's office said in a statement.

The prosecutor's office said the suspect had made extensive statements during a police hearing, but had denied the offence.

"We have the wrong man," the Die Welt newspaper had quoted a senior police chief as saying in regards to the Pakistani national arrested on Monday. "And therefore a new situation. The true perpetrator is still armed, at large and can cause fresh damage," the paper quoted the source as saying.

Police had said on Twitter: "The temporarily arrested suspect denies the offence. Therefore we are particularly alert. Please be also alert."

The temporary arrested suspect denies the offense. Therefore we are particulary alert. Please be also alert.#Breitscheidplatz

A security source said the arrested man was 23 years old, was known to police for minor offences, and had been staying at the disused Tempelhof airport, which had been turned into a refugee reception centre.

"He denies the act," interior minister Thomas de Maiziere said on Tuesday, adding that the suspect had arrived in Germany on 31 December 2015 seeking asylum.

Christmas markets in Berlin were shut for a day out of respect for victims and their relatives, but de Maiziere said the markets or major events elsewhere must continue.

"Cancelling them would be wrong," he said.

Chancellor Angela Merkel said on Tuesday: "There is much we still do not know with sufficient certainty but we must, as things stand now, assume it was a terrorist attack."

"I know it would be especially hard for us all to bear if it were confirmed that the person who committed this act was someone who sought protection and asylum."

However, police and security forces across Europe are on high alert, particularly after indications that the Christmas market attacker may be armed and on the run.

A train station in Cologne, close to Germany's border with France, was evacuated on Tuesday evening after a false alarm about a bomb threat.